0,2

If X_1,X_2,...,X_n is a partition of a 2n-set X into 2-blocks then, for n>5, a(n-6) is equal to the number of (n+6)-subsets of X intersecting each X_i (i=1,2,...,n). - Milan R. Janjic (agnus(AT)blic.net), Jul 21 2007

With a different offset, number of n-permutations (n>=6) of 3 objects: u, v, z with repetition allowed, containing exactly six (6) u's. Example: a(1)=14 because we have uuuuuuv, uuuuuvu, uuuuvuu, uuuvuuu, uuvuuuu, uvuuuuu, vuuuuuu. uuuuuuz, uuuuuzu, uuuuzuu, uuuzuuu, uuzuuuu, uzuuuuu, zuuuuuu - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 16 2008

H. Izbicki, Ueber Unterbaeume eines Baumes, Monatshefte f\"{u}r Mathematik, 74 (1970), 56-62.

Milan Janjic, Two Enumerative Functions

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

a(n)=2*a(n-1)+A054849(n-1)

G.f.: 1/(1-2x)^7.

A002409:=-1/(2*z-1)**7; [S. Plouffe in his 1992 dissertation.]

seq(binomial(n+6, 6)*2^n, n=0..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 16 2008

Cf. A000079, A001787, A001788, A001789, A003472, A054849, A054851, A038207.

For n>0, a(n) = 2 * A082140(n). First differences are in A006976.

Sequence in context: A036395 A039630 A004408 this_sequence A007817 A044346 A044727

Adjacent sequences: A002406 A002407 A002408 this_sequence A002410 A002411 A002412

easy,nonn

njas

More terms from Henry Bottomley (se16(AT)btinternet.com) and James A. Sellers (sellersj(AT)math.psu.edu), Apr 15 2000

Typo in definition corrected by Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 16 2008